Anisotropic materials have unequal physical properties along different axes. Optically anisotropic materials are typically birefringent. That is, light waves are split upon entry into the anisotropic material into two waves with differing velocities and hence different refractive indices. An example of an optically anisotropic material is a polymeric film such as polyester.
An optical characteristic of an anisotropic material is optical retardation. Optical retardation is defined as the product of thickness and birefringence. More particularly: EQU R=t * birefringence Equation 1
Written alternatively, EQU R=t * (n.sub.1 -n.sub.2) Equation 2
wherein:
t is thickness,
n.sub.1 is the index of refraction in a first direction, and
n.sub.2 is the index of refraction in a second direction perpendicular to the first direction.
Apparatus and methods exist for determining the birefringence of a material. For example, German Patent No. DE 23 38 305 C3 (Frangen) discloses a method for determining the linear birefringence of a material, particularly in a form suitable for use in process control. Using transmission, Frangen teaches a first polarizer upstream of the material, and a second polarizer downstream of the material whose plane of polarization is perpendicular to that of the first polarizer. A photoelectrical receiving unit downstream of the second polarizer detects the wavelengths to determine birefringence. A separate thickness measuring device is provided.
A reference titled, "Determination of Orientation in Thermotropic Liquid Crystalline Polymer Films for Spectrographic Measurement of the Birefringence", by Beekmans and de Boer, Macromolecules, Vol 29, No. 27, American Chemical Society, 1996, teaches a transmission apparatus suitable for determining birefringence. FIG. 1 illustrates the optical setup for spectrographic birefringence measurements. A light source 10 directs light through a lens 12 and a first polarizer 14 onto sample 16. The light is transmitted through sample 16 and second polarizer 18, and impinges a diode array 20 of a detector 22. The wavelengths of the light impinging diode array 20 are analyzed by a computer 24.
An apparatus for measuring thickness and the index of refraction is commercially available from FILMETRICS of San Diego, Calif. FILMETRICS' product F20 determines film thickness and wavelength-dependent optical constants by acquiring reflectivity values at 512 wavelengths. Product literature identifies the performance specifications for a sample thickness range of 10 nm to 50 .mu.m. Referring to FIG. 2, light from light source 20 is directed along a fiber optic cable 26 and through a lens 28 onto sample 16. The light is reflected back through fiber optic cable 26 into a spectrometer 30 where the reflected light is analyzed.
It may be desirable to determine only retardation, and not the specific values of thickness and/or birefringence. Therefore, while the German apparatus and the Beekmans and deBoer apparatus may have achieved a certain level of success, they afford a complex solution for Applicant's particular application. The FILMETRICS apparatus also does not provide an apparatus and method for determining retardation directly.
As such, a need continues to exist for an apparatus and method for determining retardation directly, that is, without determining the specific values of thickness and birefringence. A suitable apparatus is preferably simple in design, transportable, and compact in size. A suitable method is robust, consistent, and provides analysis results quickly.